Multivariate Rough Volatility

Ranieri Dugo (), Giacomo Giorgio () and Paolo Pigato
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Ranieri Dugo: DEF, University of Rome "Tor Vergata", http://www.ceistorvergata.it
Giacomo Giorgio: Dept of Mathematics, University of Rome "Tor Vergata"

No 589, CEIS Research Paper from Tor Vergata University, CEIS

Abstract: Motivated by empirical evidence from the joint behavior of realized volatility time series, we propose to model the joint dynamics of log-volatilities using a multivariate fractional Ornstein-Uhlenbeck process. This model is a multivariate version of the Rough Fractional Stochastic Volatility model proposed in Gatheral, Jaisson, and Rosenbaum, Quant. Finance, 2018. It allows for different Hurst exponents in the different marginal components and non trivial interdependencies. We discuss the main features of the model and propose an estimator that jointly identifies its parameters. We derive the asymptotic theory of the estimator and perform a simulation study that confirms the asymptotic theory in finite sample. We carry out an extensive empirical investigation on all realized volatility time series covering the entire span of about two decades in the Oxford-Man realized library. Our analysis shows that these time series are strongly correlated and can exhibit asymmetries in their cross-covariance structure, accurately captured by our model. These asymmetries lead to spillover effects that we analyse theoretically within the model and then using our empirical estimates. Moreover, in accordance with the existing literature, we observe behaviors close to non-stationarity and rough trajectories.

Keywords: stochastic volatility; rough volatility; realized volatility; multivariate time series; volatility spillovers; mean reversion. (search for similar items in EconPapers)
JEL-codes: C32 C51 C58 G17 (search for similar items in EconPapers)
Pages: 35 pages
Date: 2024-12-20, Revised 2024-12-20
New Economics Papers: this item is included in nep-ecm and nep-ets
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Working Paper: Multivariate Rough Volatility (2024)
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